1. Kepler’s Laws Newton’s Law of Universal Gravitation was based on the work of Johannes Kepler.

2. Kepler’s 3 laws: 1.Planets move in elliptical orbits with the sun at one focus.

3. Kepler’s 3 laws: 2.A line joining the sun and a planet sweeps out equal areas in equal times Note: this means that planets must travel faster when it is near the sun, and slower when it is farthest

4. Kepler’s 3 laws: 3.The following ratio is the same for all the planets or satellites which orbit around the same central body Where R = radius of orbit (metres or astronomical units) And T = period of orbit Note: 1 AU = average radius of Earth orbit = 1.49 x 10 11 m Click here for more info on AUhere

5. *K sun = = 3.35 x 10 18 m 3 /s 2 All objects orbiting the sun have this ratio of radius cubed to period squared.

6. Sample 1: How fast in m 2 /s is an area being swept out by a line joining the Earth and the sun?

7. Sample 2: A planet in our solar system has a period of revolution of 7.6 x 10 6 seconds. Find the radius of the planet’s orbit and identify the planet from the table in the booklet.

8. K sun = The planet is Mercury

9. Sample 3: Mars has a radius of orbit of 1.52 astronomical units, and revolves around the sun once every 690 days. If Venus has an orbit of radius of 0.72 AU, how long does it take Venus to go around the sun?

11. Read textbook pages 217 – 220 for more info on Kepler’s Laws.